Problem: Given $ m \angle AOB = 7x + 30$, $ m \angle BOC = 9x + 42$, and $ m \angle AOC = 104$, find $m\angle BOC$. $O$ $A$ $C$ $B$
Explanation: From the diagram, we see that together ${\angle AOB}$ and ${\angle BOC}$ form ${\angle AOC}$ , so $ {m\angle AOB} + {m\angle BOC} = {m\angle AOC}$ Substitute in the expressions that were given for each measure: $ {7x + 30} + {9x + 42} = {104}$ Combine like terms: $ 16x + 72 = 104$ Subtract $72$ from both sides: $ 16x = 32$ Divide both sides by $16$ to find $x$ $ x = 2$ Substitute $2$ for $x$ in the expression that was given for $m\angle BOC$ $ m\angle BOC = 9({2}) + 42$ Simplify: $ {m\angle BOC = 18 + 42}$ So ${m\angle BOC = 60}$.